Journal of the Indonesian Mathematical Society

Representation Matrices of Coprime Graph of Generalized Quaternion Group

Siti Zahidah, Ahmad Nadimas Zulfikar, Nenik Estuningsih, Ahmad Erfanian — Thu, 14 Aug 2025 00:00:00 +0000

This study discusses the representation matrices of coprime graph of generalized quaternion group. The representation matrices are adjacency matrix, antiadjacency matrix, Laplacian matrix, and signless Laplacian matrix. Furthermore, the eigenvalues of each representation matrices are determined. As the results, we obtained the construction of the four representation matrices and their eigenvalues. Based on the matrix form, we got the matrix determinant is zero, so that the matrices have zero eigenvalues except signless Laplacian matrix. As for the non-zero eigenvalues, the values depends on the type of representation matrices and the order of the graph as well as its algebraic multiplicity.

On Basic Ideal Generated by Vertices in Cycles without Exits in Leavitt Path Algebras

Khurul Wardati, Aulia Khifah Futhona — Thu, 14 Aug 2025 00:00:00 +0000

Vertices located on cycles without exits have a role in constructing ideals in the Leavitt path algebras over a commutative unital ring. One key reason is that the set of such vertices is hereditary. In addition, an ideal of the commutative unital ring can be combined with these vertices to form an ideal in the Leavitt path algebra. This article focuses on creating a (basic) ideal in the Leavitt path algebras, which is generated by vertices on cycles without exits.

Semiparametric Bivariate Probit Model Early Breastfeeding Initiation and Exclusive Breastfeeding

Suci Amalia, Vita Ratnasari, Ismaini Zain — Thu, 14 Aug 2025 00:00:00 +0000

Regression analysis in which the response variable is categorical can be processed using the probit model. The probit model is based on the normal distribution, in addition to its interpretation based on marginal effect values. A probit model consisting of two response variables is called the bivariate probit model, in which the response variables each consist of two categories. The predictor variables in bivariate probit model can be either categorical and also continuous data. Bivariate probit model both response variables have a relationship. One of the developments of the bivariate probit model is the semiparametric bivariate probit model, where the bivariate probit model in which there is a parametric and a nonparametric model in this case in the form of a continuous covariate smooth function. Semiparametric bivariate probit model have the advantage of being able to address the problem of nonlinearity of undetected continuous predictor variables that can cause modeling inaccuracies that can effect the results of estimation accuracy. Parameter estimation of semiparametric bivariate probit model uses the Penalized Maximum Likelihood Estimation approach, but the equation obtained is not closed form so iteration are needed to solve it. The iteration used is Fisher Scoring. The semiparametric bivariate probit model was applied to data on early breastfeeding initiation and exclusive breastfeeding in East Java Province in 2021 with variables that affect early breastfeeding initiation being birth attendants while those affecting exclusive breastfeeding are maternal age and maternal education level.

Diachromatic Number of Some Acyclic Digraphs

Raventino Raventino, Yeni Susanti — Thu, 14 Aug 2025 00:00:00 +0000

A vertex coloring that ensures every pair of different colors is represented at least once is termed complete coloring. The diachromatic number of an acyclic digraph denotes the maximum number of colors required for its complete coloring. This study delves into the diachromatic numbers of lobster digraphs, fireworks digraphs, banana tree digraphs, and coconut tree digraphs under specific and arbitrary directional orientations.

On Sombor Energy of the Nilpotent Graph of the Ring of Integers Modulo ε

Lalu Riski Wirendra Putra, Jimboy R. Albaracin, I Gede Adhitya Wisnu Wardhana — Thu, 14 Aug 2025 00:00:00 +0000

In chemical graph theory, chemical compounds are represented as graphs where atoms are represented as vertices, and the bonds connecting the atoms are represented as edges. In 2021, Gowtham and Swamy discovered another type of graph energy, called the Sombor energy. This discovery was motivated by Gutman's introduction of the Sombor index in the same year. In the field of abstract algebra, rings can also be represented as graphs. In this article, we aim to explore the Sombor energy of some nilpotent graphs of rings, particularly the ring of integers modulo ε.

An Imprecise High-Order Fuzzy Time Series Model Forecasting the Stocks Traded Using Central-Log-Ratio Transformation of Compositional Data

Muhammad Shahbaz Khan, Mir Ghulam Hyder Talpur, Muhammad Aslam — Thu, 14 Aug 2025 00:00:00 +0000

Malaysia, Indonesia, and Thailand countries have half of the trade in the group of the Association of Southeast Asian Nations (ASEAN) members. An agreement has increased the importance of trade coalition without the US dollar among them. To understand the pattern of the Stock Traded in these countries, this study developed ample fuzzy time series foretelling models. An innovative data transformation approach called compositional data is employed. The Fuzzy Time series models are implemented with different orders of fuzzy logical relationships. The Trapezoidal and Spline S-shaped membership functions are engaged in these models. The performance of forecasting is evaluated through the compositional root mean square error (CRMSE) and compositional mean absolute percentage error (CMAPE). The analysis of forecasted accuracy measurements showed that the Third-Order Fuzzy Time Series model with a Trapezoidal membership function outclassed other orders models. It is also observable that Thailand's stock traded values increased compared to Malaysia and Indonesia.

Soft S-Paracompact Space

Vishwanath Kumasi, Baiju Thankachan — Thu, 14 Aug 2025 00:00:00 +0000

This paper introduces a new topological class called soft S-paracompact spaces. These spaces generalize the concept of soft paracompact spaces. A soft topological space is considered soft S-paracompact if every soft open cover has a locally finite soft semi-open refinement. We explore the key properties of soft S-paracompact spaces and investigate their relationships with other well-established soft topological spaces. We depict an application of soft S-paracompactness in the decision-making problem.

Implementation of Dual Reciprocity Boundary Element Method to Solve The Mathematical Model of Steady Infiltration in Heterogeneous Soils Vertically

Armando Deminto Paa, Imam Solekhudin — Thu, 14 Aug 2025 00:00:00 +0000

The Dual Reciprocity Boundary Element Method (DRBEM) is applied to Richards' equation for steady infiltration in unsaturated soil. The types of soil observed are Guelph Loam (GL) and Pima Clay Loam (PCL). A mathematical model for infiltration in heterogeneous unsaturated soil is built using Richards' equation and the Gardner model, with GL and PCL soil parameters. The heterogeneous soil types include GL-PCL and PCL-GL, where each soil is assumed to vary linearly in the vertical direction. This study investigates infiltration in vertically heterogeneous soils. Using DRBEM, the numerical simulation results of hydraulic conductivity are obtained as an approximation of the constructed mathematical model. Based on the numerical results of the hydraulic conductivity, the soil water potential values can be calculated using the Gardner model. The results of this study provide the distribution of the water content under steady-state conditions in heterogeneous soils, determined by hydraulic conductivity and soil water potential.

Bipolar Fuzzy Filters in BL-Algebras

Manal Abdullah Alqahtany, Tanisha Bhagwan Dale — Wed, 20 Aug 2025 00:00:00 +0000

This research introduces and examines the novel concept of filters in BL-algebras constructed upon bipolar fuzzy structures. Specifically, we present the formulation of bipolar fuzzy filters (BFFs) within the context of BL-algebras and conduct a comprehensive investigation of their associated properties. This work extends the traditional notion of filters in BL-algebras by incorporating the bipolarity aspect of fuzzy logic, thereby providing a more nuanced framework for analyzing logical structures. Our study not only establishes the fundamental definitions but also explores the theoretical implications and characteristics of these bipolar fuzzy filters, contributing to the broader understanding of many-valued logic systems and their algebraic representations.